Simulating the generation, evolution and fate of electronic excitations in molecular and nanoscale materials with first principles methods. 1. Our team and our code 2. Background and motivation 3. Physical science goals and strategy 4. Math and comp. sci. goals and strategy
Our team of 8 Daniel Haxton (Chemical Sciences, LBNL). Role: Electronic structure theory Martin Head-Gordon (Chemical Sciences, LBNL). Role: Electronic structure theory Anna Krylov (Chemistry, USC). Role: Electronic structure theory Xiaoye (Sherry) Li (Computational Res., LBNL). Role: Numerical linear algebra
Our team of 8 C. William McCurdy (Chemical Sciences, LBNL). Role: Electronic structure theory Esmond Ng (Computational Research, LBNL). Role: Numerical linear algebra Chao Yang (Computational Research, LBNL). Role: Numerical linear algebra Samuel Williams (Computational Res., LBNL). Role: Parallelization
Q-Chem: Our code. Est. 1993. Commercial code, academic control. Over 3 million lines of code: C++ and Fortran. Over 200 active developers: Open TeamWare. Over 55,000 distributed copies: Q-Chem/Spartan. Broad range of capabilities * Density functional theory * Coupled cluster theory * Unique specialized methods * Parallel capabilities using MPI and OpenMP
And one more key person... Evgeny Epifanovsky (LBNL / USC / Q-Chem). Role: Tensor library and decompositions He will be a key player in our work, connecting activity at USC, Berkeley and Q-Chem. Evgeny is here, presenting a poster on Tuesday: General Block-Tensor Library for High-Level Electronic Structure Calculations
Simulating the generation, evolution and fate of electronic excitations in molecular and nanoscale materials with first principles methods. 1. Our team and our code 2. Background and motivation 3. Physical science goals and strategy 4. Math and comp. sci. goals and strategy
Computer-based simulations of excited states... As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. Albert Einstein What goes into the simulation? (1) An approximate quantum treatment (e.g. what we will be working on!) (2) A model of the (remote) environment (e.g. 100 s/1000 s of MM atoms) (3) Surface walking approach (e.g. classical trajectories or stat mech., )
Goal of quantum chemistry: Stationary states of the Schrodinger equation... Ĥ = i 1 2 2 i + V ext r i i ( ) + 1 2 i j r i r j 1 Ĥ j j ( r 1,r 2,Kr ) n = E j ( j r 1,r 2,Kr ) n ( r 2,r 1,Kr ) n = ( j r 1,r 2,Kr ) n This involves exponential computational effort as a function of the number of electrons... Approximations are imperative... Tremendous progress for ground states Excited state approximations are less developed
Examples of interesting problems: bound excited states. Natural and artificial light-harvesting: (1) Carotenoids: (2) Acene organic crystals:
Bound excited states: Status / challenges. Methods are available for bound excited states in large molecules (TDDFT, CIS). However, they fail for many problems of interest, and cannot be systematically improved. E.g. Both the carotene and acene examples Systematically improvable methods are available for the types of excited states that occur in those examples (CASSCF, CASPT2) But they are typically very expensive. There is a need for systematically improvable models at low enough cost to treat large systems.
Examples of interesting problems: Unbound excited states. Transient electron attachment: (1) Resonances / reactions / chemistry from secondary electrons: (2) Transient species in ultrafast experiments: Probing resonances / resonances as probes
Unbound excited states: Status / challenges. Powerful formal theories (complex scaling) have been developed to obtain both the real and imaginary part of the energy for unbound states. These methods have been implemented in codes and applied to small systems (atoms, diatomics and small molecules) over the past 30 years. There is a need to leverage the power of bound state quantum chemistry to resonances.
Simulating the generation, evolution and fate of electronic excitations in molecular and nanoscale materials with first principles methods. 1. Our team and our code 2. Background and motivation 3. Physical science goals and strategy 4. Math and comp. sci. goals and strategy
Physical science goals: Bound states (1) Develop new methods and software for bound excited states of large molecules (up to 200-500 atoms). Approach: Extend the restricted active space spin-flip method. Obtain higher accuracy by correcting for dynamic correlation (Head-Gordon). H ( 0) c = c H ( 0+1+2 ) c = c i RAS SF = c i A,h,p ( ) ( 0 = H ) PP + ( 1) ( 1 V PQ F ) ( ) QQ E 0 + P ˆV 1 0+1+2 H PP Q ( ) 1 V QP 1 ( ) ˆ ( ) Benefit: Open up a new range of large-molecule applications (e.g. aspects of natural and artificial light harvesting that are not yet well understood) T 1 P C
Physical science goals: Unbound states (2) Adapt electronic structure methods for resonance states of polyatomic molecules Approach: Complex scaled basis functions (McCurdy/HG), grid-based methods (Haxton). Benefit: No capability of this type currently exists, despite broad relevance.
Physical science goals: Reduced scaling (3) Development of reduced scaling implementations of existing coupled cluster methods for electronic excited states. Approach: Explore matrix and tensor decompositions (Krylov). Benefit: Apply these reliable and proven methods for calculating excited states to larger molecules, and apply the same underlying ideas for reduced scaling to other methods, such as those in the first two objectives.
Simulating the generation, evolution and fate of electronic excitations in molecular and nanoscale materials with first principles methods. 1. Our team and our code 2. Background and motivation 3. Physical science goals and strategy 4. Math and comp. sci. goals and strategy
CS enabling goals: Tensor library (1A) Develop and refine an object-oriented tensor library, both for real variables (bound states), and for the complex variables (resonance states), and including compact decompositions for low scaling. Enables implementation of models. Will be made publicly available. (1B) Parallelize the tensor library via a distributed hybrid approach (MPI+threads) targeted for leadership class computers (and flexible enough to perform well on mid-range clusters) (Williams). Enables achievement of application goals.
Math goals: Decompositions (1) Explore and implement rank reduction and compression schemes for the tensors that arise in excited state electronic structure calculations. Enable their use to develop reduced scaling excited state methods. Approach: CPD, TT, Iterative subspace sampling, Cholesky. Compare effectiveness for different tensors that arise. Explore combinations.
Math enabling goals: Eigensolvers (2A) Deploy efficient eigensolvers for the symmetric real eigenvalue problems that yield bound excited state energies. PARPACK will improve efficiency (2B) Extend and develop eigensolvers for the complex eigenvalue problems that arise in treating resonance states. New capabilities: Jacobi-Davidson, subspace iteration, contour integral-based (2C) Provide robust linear solvers and effective preconditioners to support the eigenvalue solvers. Hybrid linear solver PDSLin, low-rank approximation preconditioners
Other key issues (1) Relationship to the SciDAC Institutes. FASTMath: synergy & extension (Li, Ng, Yang). SUPER: parallelization activities (Williams). (2) Verification and validation. Automatic multiplatform testing, > 200 test jobs UQ does not directly enter (but recall quote). (3) Software sustainability. Q-Chem has survived & grown over 19 years. Much to learn about code (re)structuring! Paid user base supports code maintenance.
Simulating electronic excitations in molecular and nanoscale materials with first principles methods. lightharvesting molecular design UV damage physical science: models calculating bound excited states & resonances applied math: solvers computer science: HPC